1. Field of the Invention
The present invention is directed to methods for determining electron transfer rates in systems containing metalloproteins. Such methods may be used, for example, to model the electron transfer rate between a metalloprotein and a substrate or the self-exchange rate of a metalloprotein and based on the model to design drugs and engineer proteins tailored to enhance or diminish the efficiency of catalytic processes.
2. Background of the Related Art
Propagation of the spin of an unpaired electron through space is referred to as spin diffusion. Spin diffusion can be treated similarly to physical diffusion of molecules. As a spin diffuses through space, the induced magnetization is transferred through space. Magnetization is analogous to concentration, and changes in space as a function of time. Like mass transfer, magnetization transfer through a molecule is characterized by a spin diffusion coefficient (D). Like Fick's Law for mass transfer, magnetization transfer is defined by the modified Bloch equations [48]. The Bloch equation for magnetization transfer through both the process of relaxation and spin diffusion is shown in Equation 1.
                                          ∂            M                                ∂            t                          =                                            g              ⁢                                                          ⁢              β              ⁢                                                          ⁢                              M                ·                H                                      ℏ                    +                      D            ⁢                                          ∇                2                            ⁢              M                                                          (        1        )            where M is the magnetization, H is magnetic field, β is the Bohr magneton, and g is the electronic g factor. The spin diffusion coefficient is equal to Wa2, where W is the spin flip-flop probability pet second (˜103sec−1) and a is the nearest neighbor distance. The actual value of the spin flip-flop probability per second is equal to one fiftieth of the inverse of the spin-spin relaxation time,
  W  =            1              50        ⁢        T              .  
Paramagnetic metal centers of proteins can induce large magnetic fields. However, the decay length of the field is less than the distance between the metal center and the surface active site. Thus, the field at the substrate is well approximated as that of the earth's magnetic field. Because protein/substrate electron transfer reactions occur within the earth's magnetic field, the spin relaxation portion of the Bloch equation (gβM·H/) is negligible. The Bloch equation then simplifies to Equation 2, which is directly analogous to Fick's second law. The spin diffusion coefficient is a function of the overall conjugation of the protein and the existing electron withdrawing groups.
                                          ∂            M                                ∂            t                          =                  D          ⁢                                    ∇              2                        ⁢            M                                              (        2        )            
If the electron transfer between protein and substrate occurs though a spin polarization pathway, the spin must diffuse from the metal center to the surface active site before spin polarization can occur. Therefore, the electron transfer will occur in two steps; the first step is spin diffusion to the surface active site and the second step is the spin polarization/electron transfer. The overall electron transfer rate will be a function of these two steps.
One third of all proteins are metalloproteins. Metalloproteins include a metal center, such as Fe, Ca, Cu or Zn, and a protein structure, typically composed of elements such as carbon, nitrogen, oxygen, hydrogen and sulfur, surrounding the metal center. For instance, hemoglobin, which carries oxygen in the bloodstream, is an iron containing metalloprotein.
Two areas where electron transfer reactions may be important are smart drug design and enzyme engineering.
In enzyme engineering, the structure of an enzyme is altered to change its catalytic rates and processes. This may be done, for instance, to increase rates and thus product generation. Similarly, an enzyme could be engineered to avoid making unwanted side products.
In drug design, drugs are designed that act as a substrate and alter the rate of an enzymatic reaction, either faster or slower. The substrate might, for instance, block the active site.
Prior art methods for determining the electron transfer rates of metalloproteins have been shown to be inaccurate. For instance, electron transfer rates determined according to conventional Marcus Theory typically differ from experimentally observed values by four to seven orders of magntitude.
Therefore, there exists a need in the art for a method by which to model electron transfer rates in metalloprotein systems more accurately. Examples include metalloprotein/substrate electron transfer rates and metalloprotein self exchange rates.